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What is the variance of the random variable X?
For a discrete random variable X, the variance of X is obtained as follows: var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function pX(x) of X.
What does variance of x mean?
By definition, the variance of X is the average value of (X−μX)2. Since (X−μX)2≥0, the variance is always larger than or equal to zero. A large value of the variance means that (X−μX)2 is often large, so X often takes values far from its mean. This means that the distribution is very spread out.
What is the formula for variance of X?
Definition: If X is a random variable with mean E(X) = µ, then the variance of X is defined by Var(X) = E((X − µ)2). The standard deviation σ of X is defined by σ = Var(X).
What is a variance of a discrete random variable?
A measure of spread for a distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value. The square root of the variance is equal to the standard deviation. …
How is the variance of a random variable calculated?
In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected value). Notice that the variance of a random variable will result in a number with units squared, but the standard deviation will have the same units as the random variable.
Which is the correct definition of the variance of X?
By definition, the variance of X is the average value of (X − μ X) 2. Since (X − μ X) 2 ≥ 0, the variance is always larger than or equal to zero. A large value of the variance means that (X − μ X) 2 is often large, so X often takes values far from its mean. This means that the distribution is very spread out.
What are the properties of variance of a variable?
Properties of Variance The variance has properties very different from those of the expectation. If c is any constant, E(cX) = cE(X) and E(X + c) = E(X) + c. These two statements imply that the expectation is a linear function.
Which is better the variance or the standard deviation?
Notice that the variance of a random variable will result in a number with units squared, but the standard deviation will have the same units as the random variable. Thus, the standard deviation is easier to interpret, which is why we make a point to define it. The variance and standard deviation give us a measure of spread for random variables.